Glasses lens designing method, production method for glasses lens and computer program

ABSTRACT

1  indicates the rotating point of the eyeball,  2  indicates the first eye position,  3  indicates the second eye position, and  4  indicates the third eye position. The lines indicated by thick lines at the respective eye positions are the horizontal meridian and vertical meridian (principal meridian) of the cornea. As is seen from the figure, the directions of the horizontal meridian and vertical meridian of the cornea at the third eye position  4 , in particular, do not coincide with the directions of the horizontal meridian and vertical meridian at the first eye position  1 . In the present means, in order to perform aberration correction of the ophthalmic lens not only in the first eye position and second eye position but also in the third eye position under conditions that are suited to the prescription of the user and conditions of use, the prescription surface is made aspherical while taking into account the astigmatic axis of the eye at arbitrary eye positions in accordance with the laws of Donders-Listing. As a result, the prescription surface can be designed so that favorable optical characteristics can be obtained in the case of various specifications involving individual information such as the prescription of the ophthalmic lens user.

TECHNICAL FIELD

The present invention relates to an ophthalmic lens design method, anophthalmic lens manufacturing method, and a computer program used inophthalmic lens design.

BACKGROUND ART

Generally, the relationship between the apical curvature of anophthalmic lens at which the astigmatic aberration of the light rayspassing through the lens shows a minimum value and the apical refractivepower on the optical axis of the lens (hereafter referred to as the“dioptric power”) can be obtained, for example, from the Tscherningellipse.

Specifically, it is well known that the occurrence of astigmaticaberration in the peripheral parts of the lens can be suppressed byadjusting the curvatures of both refractive surfaces of the lens to anoptimal combination obtained by means of this Tscherning ellipse, andthe optical performance drops conspicuously if a combination ofcurvatures of both refractive surfaces that departs greatly from thisTscherning ellipse is selected.

However, in cases where an optimal combination of curvatures of bothrefractive surfaces obtained by means of this Tscherning ellipse isused, the curvatures of the refractive surfaces of the lens surfaces areincreased, and the thickness of the lens also tends to increase.

Accordingly, in ophthalmic lenses seen in recent years, because ofproblems in terms of reducing the lens thickness and problems in termsof external appearance, and also for convenience of manufacture and thelike, curvatures that are smaller than the curvatures obtained by theoptimal combination of curvatures have been selected in almost all casesas the refractive surface curvatures (hereafter called the “base curve”)of lens surfaces on the object side (hereafter called the “outersurfaces”).

Specifically, in cases where problems of optical performance andexternal appearance are taken into account, the practical range of thebase curve of an ophthalmic lens is limited to a specified range inaccordance with the dioptric power of the ophthalmic lens. Furthermore,in cases where the refractive surfaces are constructed only fromspherical surfaces, it is impossible to solve the problems ofmaintaining the optical performance in the desired range and improvingthe external appearance at the same time. Currently, therefore, lensesin which astigmatic aberration and dioptric power error in theperipheral parts of the lens are corrected while reducing the curvatureof the base curve and maintaining the thickness of the lens at a smallvalue mainly by making one of the refractive surfaces of the lensaspherical constitute the mainstream of lenses.

Ordinarily, in the principal rays passing through the ophthalmic lenscorresponding to the line of sight of the user, the astigmaticaberration of the principal rays can be expressed as follows where Dmaxis the maximum principal refractive power and Dmin is the minimumprincipal refractive power.|Dmax−Dmin|Furthermore, the mean refractive power of the principal rays can beexpressed as follows:(Dmax+Dmin)/2These are treated as important factors in the design of the ophthalmiclens. Accordingly, in conventional ophthalmic lenses, the correction ofaberration has been accomplished using such astigmatic aberration, meanrefractive power, maximum principal refractive power and minimumprincipal refractive power as parameters.

Incidentally it is a well-known fact that the refractive power in thedirection of an arbitrary meridian on a plane perpendicular to theprincipal rays has maximum and minimum values, and that the meridiandirections that give these maximum and minimum values are perpendicularto each other. Accordingly, in the present specification, the maximumvalue of the refractive power in these arbitrary principal rays is takenas the maximum principal refractive power, the minimum value of thisrefractive power is taken as the minimum principal refractive power, andthis maximum principal refractive power and minimum principal refractivepower are referred to collectively as the principal refractive power.

Furthermore, the direction of the principal meridian including themaximum principal refractive power is taken as the maximum principaldirection, the direction of the principal meridian including the minimumprincipal refractive power is taken as the minimum principal direction,and the maximum principal direction and minimum principal direction arereferred to collectively as the principal direction. Moreover, in thepresent invention, the units of the values that express the refractivepower are all diopter units unless otherwise specifically noted.

In a conventional ophthalmic lens, because of the need for costreduction and simplification from the standpoint of manufacture, asemi-product lens (hereafter referred to as a semi-finished lens) inwhich one of the refractive surfaces of the lens has been workedbeforehand is used. The refractive surface that has not been workedbeforehand is called the prescription surface. Specifically, by workingthe prescription surface of the semi-finished lens into a spherical ortoric surface in accordance with the prescription of the ophthalmic lensuser, it is possible to use the same semi-finished lens in common in afixed diopter range. Accordingly, this plays a large role in costreduction (reduction of working costs, warehousing, and the like).

Ordinarily, the shape of the refractive surface of the semi-finishedlens whose working is finished beforehand is a spherical surface shapeor an aspherical surface shape that is rotationally symmetrical withrespect to the optical axis, and this spherical surface shape oraspherical surface shape is set as a spherical or aspherical surfaceshape with respect to a certain specified dioptric power within thecommon dioptric power range so that the aberration shows a minimumvalue. If this set dioptric power is taken as the standard dioptricpower for this semi-finished lens, then the optical performance of thelens in the dioptric power range in the vicinity of this standarddioptric power is favorable; however, in a dioptric power range that isremoved from this standard dioptric power, a deterioration in theoptical performance especially in the peripheral parts of the lenscannot be avoided. Furthermore, the following drawback is alsoencountered: namely, in cases where correction of astigmatism isnecessary, even if the dioptric power is the standard dioptric power, adeterioration in the optical performance in the peripheral parts of thelens cannot be avoided.

Recently, however, because of the development of techniques for freelyworking aspherical surfaces, it has also become possible to correctaberration by forming prescription surfaces that have conventionallybeen spherical or toric surfaces into aspherical surfaces, so thatophthalmic lenses in which the conditions of use by the user are takeninto account and the prescription surfaces are made aspherical have beendeveloped into products.

However, especially in the case of ophthalmic lenses that involvecorrection of astigmatism, the astigmatic dioptric power according tothe prescription is included in the astigmatic aberration of the lens,and the principal direction of the astigmatic axis of the eye, whichvaries with the movement of the line of sight, must be taken intoaccount.

In order to provide an ophthalmic lens that is optimal for theindividual user in accordance with specifications and conditions of usethat vary with each user, the mere evaluation of the optical performanceaccording to the meridional image plane and sagittal image plane,astigmatic aberration and mean refractive power conventionally used inthe design of ophthalmic lenses is insufficient. In addition to theconventional evaluation of optical performance, torsion along theastigmatic axis of the eye and the principal direction of the principalrefractive power of the lens must be taken into account, and a pluralityof different types of optical performance must be simultaneouslyimproved, in order to provide an ophthalmic lens that is optimal foreach individual user. However, a so-called trade-off relationship mayexist among different types of optical performance; consequently, it isdifficult to reduce all aberration to a minimum value. Accordingly, itis necessary to achieve a refractive surface design which is such that abalance is obtained between different types of optical performance, sothat an optimal optical performance is obtained overall.

Conventionally, in order to obtain a balance between different types ofoptical performance, designers have considered and judged variousperformance values. However, in order to design ophthalmic lenses byoptimizing the optical performance for individual users, it is alsonecessary to automate such judgments by means of a computer.

The present invention was devised in light of such circumstances; it isan object of the present invention to provide a method for designingprescription surfaces so that a favorable optical performance can beobtained in various specifications accompanying individual informationsuch as prescriptions for ophthalmic lens users, and an ophthalmic lensmanufacturing method using this design method.

DISCLOSURE OF THE INVENTION

The first invention that is used to achieve the object described aboveis a method for designing ophthalmic lenses in which at least onesurface among the set of refractive surfaces on the object side and eyeside in the mounted state has a spherical or aspherical surface shapethat is formed beforehand, and at least one refractive surface has anaspherical surface shape, this ophthalmic lens design method beingcharacterized in that design is performed so that the shape of therefractive surface whose shape is not formed beforehand among the set ofrefractive surfaces is an aspherical surface shape which is such thatthe aberration of the ophthalmic lens is corrected according to the lawsof Donders-Listing in accordance with at least the refractive power thatis necessary for refractive correction of the user or the refractivepower that is necessary for astigmatic correction, or both.

Furthermore, in the present specification and claims, the term “whoseshape is molded (formed) beforehand” refers to the fact that the shapeof this surface is determined in the semi-product stage, so thatsubsequent working is unnecessary. Furthermore, the term “whose shape isnot formed (i.e., is not molded) beforehand” refers to the fact thatalthough molding into a specified shape is performed in the semi-productstage, it is a prerequisite that further working is required in order touse this as a final product.

The laws of Donders-Listing are laws that relate to the rotationalmotion of the eye and eye positions. In these laws, the rotationalmotion of the eye that accompanies movement of the line of sight isexpressed by a continuation of rotational motion which is performedabout a rotational axis that passes through the rotating point and thatis perpendicular to the line of sight at the first eye position; it isindicated that the arbitrary eye position that is achieved by means ofthis rotation is definitively determined regardless of the movement pathof the line of sight. Furthermore, the rotational axis of the eyeball inthis case is located on a plane that is perpendicular to the line ofsight at the first eye position, and this plane is called the Listing'splane.

FIG. 1 is a diagram which shows the positions of the eye positionsgenerated by the Donders-Listing rotation and the positions of thehorizontal meridian and vertical meridian of the cornea in this caseprojected onto the Listing's plane. In FIG. 1, 1 indicates the rotatingpoint of the eyeball, 2 indicates the first eye position, 3 indicatesthe second eye position, and 4 indicates the third eye position. Thelines indicated by thick lines at the respective eye positions are thehorizontal meridian and vertical meridian (principal meridian) of thecornea.

As is seen from FIG. 1, the directions of the horizontal meridian andvertical meridian of the cornea of the eye at the third eye position 4,in particular, do not coincide with the directions of the horizontalmeridian and vertical meridian at the first eye position 1. Accordingly,in order to perform aberration correction of the ophthalmic lens notonly at the first eye position and second eye position but also at thethird eye position under conditions that are suited to the prescriptionof the user and conditions of use, it is necessary to make theprescription surface aspherical while taking into account the astigmaticaxis of the eye at arbitrary eye positions in accordance with the lawsof Donders-Listing. Furthermore, for details concerning the laws ofDonders-Listing, see Igakushoinkan “Me no Seirigaku” [“Physiology of theEye”] (Akira Hagiwara ed.) pp. 302-304.

In the present means, the shape of the refractive surface whose shape isnot formed beforehand is designed in accordance with such laws ofDonders-Listing so that this is an aspherical surface shape thatcorrects the aberration of the ophthalmic lens in accordance with atleast the refractive power that is necessary for refractive correctionof the user or the refractive power that is necessary for astigmaticcorrection of the user, or both. Accordingly, correction of theaberration of the ophthalmic lens at the third eye position, inparticular, is appropriately performed, so that an ophthalmic lens thathas favorable optical performance overall can be designed.

The second invention that is used to achieve the object described aboveis the first invention, which is characterized in that an arbitrarymeridian of the refractive power necessary for refractive correction ofthe user is taken as a standard meridian in arbitrary principal rayspassing through the plane of the ophthalmic lens, and the shape of therefractive surface whose shape is not formed beforehand is determined sothat ΔPall expressed by Equation (1) below shows a minimum value or aspecified value or less, where E(α) is the refractive power in themeridian direction that is required for the refractive correction of theeye of the user in the meridian direction at an arbitrary angle of αfrom the standard meridian, and D(α) is the refractive power in themeridian direction of the lens.ΔPall=∫ _(α) ^(h) |ΔP(α)|dα  (1)Here, ΔP(α) is a function expressed as ΔP(α)=D(α)−E(α), and a and b arevalues that satisfy the equation b−a=nπ, where n is a natural number.

In order to consider the refractive power in the direction of anarbitrary meridian on a plane perpendicular to the line of sight,observations are performed in an x-y-z coordinate system in which the xaxis is taken in the direction of the optical axis corresponding to theline of sight, the y axis is taken in the maximum principal directionwith respect to the astigmatic axis of the eye, and the z axis is takenin the direction of the minimum principal direction [with respect to theastigmatic axis of the eye. Here, Emax is the maximum refractive powerrequired for the refractive correction of the eye, and Emin is theminimum refractive power required for the refractive correction of theeye.

Ordinarily, Emax and Emin express the refractive powers required forrefractive correction and astigmatic correction. For example, in thecase of an eye with a prescription in which the spherical surfacedioptric power S=−2.00D and the astigmatic dioptric power C=−3.00D, Emaxand Emin are expressed as Emax=−2.00 (diopter) and Emin=−5.00 (diopter).

Below, a case in which the standard meridian of the present invention istaken along the z axis will be described with reference to FIG. 2. Ifthe refractive power required for the refractive correction of the eyein the direction of a meridian at an angle of α about the x axis withreference to the z axis (hereafter referred to as the “abnormal dioptricpower of refraction”) is designated as E(α), this E(α) can be expressedas follows:E(α)=E max·sin² α+Emin·cos²α

If the refractive power of the lens in the direction of a meridian at anangle of α about the x axis with reference to the z axis is designatedas D(α) in a case where the angle formed by the maximum principalmeridian of the light rays that are incident on the eye and the minimumprincipal meridian of this eye is designated as θ, then this D(α) can beexpressed as follows:D(α)=Dmax·cos²(α−θ)+Dmin·sin²(α−θ)α and θ in this case are taken as positive in the counterclockwisedirection in the positive direction of the x axis.

Here, in the present means, in a case where the absolute value of thedifference between the abnormal dioptric power of refraction of the eyeE(α) in the direction of a meridian at an angle of α about the x axiswith reference to the z axis and the refractive power D(α) of the lensis designated as ΔP(α), the sum of ΔP(α) in the range of a≦α≦b is calledthe total residual refractive power error, and is treated as anaberration that is used in the optimization of the optical performance.

Specifically, if this total residual refractive power error isdesignated as ΔPall, then this ΔPall can be expressed by the followingconditional equation:ΔPall=∫ _(α) ^(b) |ΔP(α)|dα  (1)Here, ΔP(α) is a function that can be expressed as $\begin{matrix}{{\Delta\quad{P(\alpha)}} = {{D(\alpha)} - {E(\alpha)}}} \\{= {\left( {{{D\max} \cdot {\cos^{2}\left( {\alpha - \theta} \right)}} + {{D\min} \cdot {\sin^{2}\left( {\alpha - \theta} \right)}}} \right) -}}\end{matrix}$ (Emax  ⋅ sin²α + Emin  ⋅ cos²α)and a and b are values that satisfy [the equation b−a=nπ, where n is anatural number.

For example, assuming that ΔP(α) is such that D(α)≦E(α) in the interval[a, c], D(α)<E(α) in the interval [c, d], and D(α)≧E(α) in the interval[d, b], then ΔPall can be expressed as follows:ΔPall={∫ _(α) _(c) [D(α)−E(α)]dα+∫ _(c) ^(d) [E(α)−D(α)]dα+∫_(d) ^(b)[D(α)−E(α)]dα}

The total residual refractive power error ΔPall is the sum of ΔP(α) inthe direction of an arbitrary meridian of the eye in specified principalrays when the user has mounted the ophthalmic lens, and is a newaberration quantity which includes the residual astigmatic aberrationfelt by the eye of the user, and the residual mean refractive powererror.

Accordingly, in the present means, as a result of this total residualrefractive power error ΔPall being introduced as a new aberrationevaluation method that is used in the optimization of the opticalperformance, and this value being suppressed to zero or a small value,the optimization of a balanced optical performance can be achieved whiletaking into account the laws of Donders-Listing. Specifically, therefractive power required for refractive correction and astigmaticcorrection of the eye, and the alleviation of twisting in the respectiveprincipal directions, can be simultaneously achieved. In the presentmeans, furthermore, the automation of calculations for optimizing theoptical performance is facilitated.

This has been difficult in conventional methods for performing automatedcalculations for the optimization of astigmatic aberration andaberration arising from the mean refractive power. It is desirable touse the residual astigmatic aberration or residual mean refractive powererror in order to perform an evaluation that takes the astigmaticdioptric power of the eye into account. However, there are also manyconditions that make it impossible to achieve a favorable correction ofboth the residual astigmatic aberration and residual mean refractivepower error at the same time, and there are cases in which thecorrection of one of these aberrations causes a deterioration in theother aberration.

In order to obtain an optimal optical performance in such cases, thedesigner must consider the permissible values of both of theseaberrations, and strike a balance between these aberrations. However, itis difficult to correct the residual astigmatic aberration and residualmean refractive power error, which may adopt various values depending onthe conditions, while taking into account the overall balance of theoptical performance. Especially in the case of a system in whichcalculations for optimizing the optical performance are automaticallyperformed for each order without any need for human judgment by thedesigner or the like during the optimization calculations, it isdifficult to perform an automatic judgment so that stable results arealways obtained. However, by using the total residual refractive powererror in the present invention as a judgment value, it is more easilypossible to obtain a balanced favorable optical performance even in thecase of an automated optimization calculation system that does notrequire human judgment.

Furthermore, besides simulation means such as a general DLS method, itwould also be possible to use some other appropriate optimization methodas means for minimizing ΔPall. This is also true in cases wherespecified values are minimized or reduced to a specified value or lowerin the second means or third means described later.

Moreover, in the present means, ΔPall is noted in integral form;however, giving consideration to the simplification of calculations, itwould also be possible to handle ΔPall as the sum of discrete values asshown below, and it goes without saying that this method is within anequivalent scope of the present means.

Specifically, by dividing the interval of b−a=nπ and designating thedivision numbers as i, it is possible to express ΔPall as follows if βis set equal to (b−a)/i. $\begin{matrix}{{\Delta\quad{Pall}} = {\sum\limits_{m = 0}^{i}\quad{\Delta\quad{P\left( {{m\beta} + a} \right)}}}} \\{= {{\Delta\quad{P(a)}} + {\Delta\quad{P\left( {\beta + a} \right)}} + {\Delta\quad{P\left( {{2\beta} + a} \right)}} + \ldots + {\Delta\quad{P\left( {{\left( {i - 1} \right)\beta} + a} \right)}} + \quad{\Delta\quad{P(b)}}}}\end{matrix}$

In this case, by skillfully selecting the division number i, it ispossible to simplify the calculations while keeping the calculationerror of the value obtained within a practical range, and obtainingresults comparable to those of an integral form. It goes without sayingthat beginning with this method, methods performing numericalcalculations equivalent to actually performed integration are includedin an equivalent scope of the present means.

The third invention that is used to achieve the object described aboveis the first invention, which is characterized in that an arbitrarymeridian of the refractive power necessary for refractive correction ofthe user is taken as a standard meridian in arbitrary principal rayspassing through the plane of the ophthalmic lens, and the shape of therefractive surface whose shape is not formed beforehand is determined sothat ΔPav expressed by Equation (2) below shows a minimum value or aspecified value or less, where E(α) is the refractive power in themeridian direction that is required for the refractive correction of theeye of the user in the meridian direction at an arbitrary angle of αfrom the standard meridian, and D(α) is the refractive power in themeridian direction of the lens. $\begin{matrix}{{\Delta\quad{Pav}} = {\frac{1}{{b - a}}{\int_{a}^{b}{{{\Delta\quad{P(\alpha)}}}{\mathbb{d}\alpha}}}}} & (2)\end{matrix}$Here, ΔP(α) is a value obtained by dividing the total residualrefractive power error. ΔPall by |b−a| is called the mean residualrefractive index error, and this is expressed as ΔPav, ΔP(α) is afunction expressed as ΔP(α)=D(α)−E(α), and a and b are values thatsatisfy the equation b−a=nπ, where n is a natural number.

In the present means, a value obtained by dividing the total residualrefractive power error ΔPall in the second means by ≡b−a≡ is called themean residual refractive index error, and this is expressed as ΔPav.Furthermore, the shape of the refractive surface whose shape is notformed beforehand is determined so that this ΔPav is minimized.

Since a and b are values that are determined prior to the calculations,|b−a| is a constant. Consequently, the present means are basicallyequivalent to the second means, and exhibit exactly the same operationaleffects.

Furthermore, in the present means, ΔPav is noted in integral form;however, giving consideration to the simplification of calculations, itwould also be possible to handle ΔPav as the sum of discrete values asshown below, and it goes without saying that this method is within anequivalent scope of the present means.

Specifically, by dividing the interval of b−a=nπ and designating thedivision numbers as i, it is possible to express ΔPav as follows if β isset equal to (b−a)/i. $\begin{matrix}{{\Delta\quad{Pav}} = {\frac{1}{{b - a}}{\sum\limits_{m = 0}^{i}\quad{\Delta\quad{P\left( {{m\beta} + a} \right)}}}}} \\{= {\frac{1}{{b - a}}\left\lbrack {{\Delta\quad{P(a)}} + {\Delta\quad{P\left( {\beta + a} \right)}} + {\Delta\quad{P\left( {{2\beta} + a} \right)}} + \ldots + {\Delta\quad{P\left( {{\left( {i - 1} \right)\beta} + a} \right)}} + {\Delta\quad{P(b)}}} \right.}}\end{matrix}$

In this case, by skillfully selecting the division number i, it ispossible to simplify the calculations while keeping the calculationerror of the value obtained within a practical range, and obtainingresults comparable to those of an integral form. It goes without sayingthat beginning with this method, methods performing numericalcalculations equivalent to actually performed integration are includedin an equivalent scope of the present means.

The fourth invention that is used to achieve the object described aboveis the first invention, which is characterized in that an arbitrarymeridian of the refractive power necessary for refractive correction ofthe user is taken as a standard meridian in arbitrary principal rayspassing through the plane of the ophthalmic lens, and the shape of therefractive surface whose shape is not formed beforehand is determined sothat at least one of the values ΔAS or ΔMP satisfying the followingconditional equations shows a minimum value or a specified value orless, where ΔPmax is the maximum value and ΔPmin is the minimum value ofΔP′(α)=D(α)−E(−in the range of a ≦α≦b or b≦α≦a, with E(α) being therefractive power in the meridian direction that is required for therefractive correction of the eye of the user in the meridian directionat an arbitrary angle of α from the standard meridian, and D(α) beingthe refractive power in the meridian direction of the lens.Here, ΔAS=|ΔPmax−ΔPmin |  (3)ΔMP=(ΔPmax+ΔPmin)/2  (4)and a and b are values that satisfy the equation b−a=nπ, where n is anarbitrary integer excluding zero.

In the present means, the difference between the abnormal dioptric powerof refraction of the eye in the direction of a meridian at an angle of αabout the x axis with reference to the z axis in FIG. 2 and therefractive power of the lens is designated as the residual refractivepower error ΔP′(α). Here, this ΔP′(α) is expressed as ΔP′(α)=D(α)−E(α),the maximum value of ΔP′(α) in the range of a ≦α≦b or b≦α≦a isdesignated as ΔPmax, the minimum value is designated as ΔPmin, and ΔPmaxand ΔPmin are viewed as the maximum value and minimum value of therefractive power error felt by the user when wearing this ophthalmiclens.

Accordingly, ΔPmax is taken as the maximum residual refractive powererror, ΔPmin is taken as the minimum residual refractive power error,and the following conditional equations are obtained from ΔPmax andΔPmin.

Where ΔAS is the residual astigmatic aberration of the ophthalmic lens,this ΔAS is expressed asΔAS=|ΔPmax−ΔPmin |  (3)Furthermore, where ΔMP is the residual mean refractive power error ofthe ophthalmic lens, this ΔMP is expressed asΔMP=(ΔPmax+ΔPmin)/2  (4)

In the present means, by using at least the residual astigmaticaberration ΔAS or residual mean refractive power error ΔMP, or both, inthe optimization of the optical performance, evaluation of theastigmatic aberration and mean refractive power excluding the astigmaticcomponent of the eye is made possible while taking the laws ofDonders-Listing into account (which is difficult in the case ofconventional aberration evaluation).

Ideally, it is desirable to minimize both the value of Equation (3) andthe value of Equation (4); however, depending on the lens conditions, itmay be impossible to realize this. In this case, the shape of therefractive surface whose shape is not formed beforehand is determined sothat one or the other of these values is minimized. Of course, underconditions which are such that the range of one of the values is withinthe permissible range, the system may also be devised so that the othervalue is minimized.

The fifth invention that is used to achieve the object described aboveis an ophthalmic lens manufacturing method which is characterized inthat this method has a process which is such that in a lens in which atleast one surface among the set of refractive surfaces on the objectside and eye side in the mounted state is a refractive surface having aspherical or aspherical surface shape that is formed beforehand, theshape of the refractive surface whose shape is not formed beforehand isdesigned in accordance with the ophthalmic lens design method accordingto any of the first through fourth inventions, and the refractivesurface whose shape is not formed beforehand is worked in accordancewith this design data.

In the present means, an ophthalmic lens with a favorable opticalperformance can be manufactured in various specifications accompanyingindividual information such as prescriptions for the ophthalmic lensusers.

The sixth invention that is used to achieve the object described aboveis a method for manufacturing an ophthalmic lens using as an elementmaterial a semi-product ophthalmic lens in which at least one surfaceamong the set of refractive surfaces on the object side and eye side inthe mounted state is a refractive surface having a spherical oraspherical surface shape that is formed beforehand, and at least onerefractive surface has an aspherical surface shape, this ophthalmic lensmanufacturing method being characterized in that this method has thesteps of attaching the semi-product ophthalmic lens to a shape workingapparatus, and working the refractive surface of the semi-product lenswhose shape has not been formed beforehand by means of the shape workingapparatus on the basis of design data obtained by the method accordingto any of the first through fourth inventions to produce a finishedproduct.

In the present means, the manufacture of ophthalmic lenses can beperformed on the basis of the determined design data even in cases wherethe location or firm where the design data is determined is different.Accordingly, even if the person performing the working does not havemeans such as a computer program for performing the design work, thisperson can entrust such design work to a person having such means forperforming design work, and can manufacture an ophthalmic lens utilizingthe results.

The seventh invention that is used to achieve the object described aboveis the sixth invention which is characterized in that the design data isdetermined at a different location from the location where the shapeworking apparatus is present, and is, transmitted to the location wherethe shape working apparatus is present via a communication device.

In the present means, the design data is transmitted via communicationmeans; accordingly, in cases where the manufacturer and designer are inmutually remote locations, e.g., in cases where the manufacturer anddesigner are firms in different countries, manufacture can be performedespecially efficiently. Arbitrary means such as inter-computercommunications by wire and facsimile can be used as communication means.

The eighth invention that is used to achieve the object described aboveis a computer program which determines the aspherical surface shape ofthe refractive surface of an ophthalmic lens, this computer programbeing characterized in that the calculation of the refractive power E(α)in the meridian direction required for refractive correction of the eyeof the user in the direction of a meridian at an arbitrary angle of αfrom the standard meridian when an arbitrary meridian of the refractivepower require for refractive correction of the user is taken as thestandard meridian is performed for each arbitrary set of principal rayspassing through the ophthalmic lens, the calculation of the refractivepower D(α) in the meridian direction of the lens is performed for eacharbitrary set of principal rays passing through the ophthalmic lens, andthe aspherical surface shape of the refractive surface is determined onthe basis of E(α) and D(α) so that the aberration of the ophthalmic lensshows a minimum value in accordance with the laws of Donders-Listing.

In the present means, ophthalmic lenses that appropriately performaberration correction at various eye positions can be designed by meansof a computer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram which shows the positions of eye positions generatedby Donders-Listing rotation and the positions of the horizontal meridianand vertical meridian of the cornea in this case projected onto theListing's plane.

FIG. 2 is a diagram which is used to illustrate the refractive power inthe direction of an arbitrary meridian on a plane perpendicular to theline of sight.

FIG. 3 is a distribution diagram of the mean residual refractive powererror ΔPav in a conventional example of an astigmatic lens.

FIG. 4 is a distribution diagram of the residual mean refractive powererror ΔMP in a conventional example of an astigmatic lens.

FIG. 5 is a distribution diagram of the residual astigmatic aberrationΔAS in a conventional example of an astigmatic lens.

FIG. 6 is a distribution diagram of the mean residual refractive powererror ΔPav in an astigmatic lens constituting an embodiment of thepresent invention,

FIG. 7 is a distribution diagram of the residual mean refractive powererror AMP in an astigmatic lens constituting an embodiment of thepresent invention.

FIG. 8 is a distribution diagram of the residual astigmatic aberrationΔAS in an astigmatic lens constituting an embodiment of the presentinvention.

BEST MODE FOR CARRYING OUT THE INVENTION

Embodiments of the present invention will be described below withreference to the figures and tables.

Table 1 shows lens data for a conventional ophthalmic lens whose objectis astigmatic correction, in which the external diameter of the lens is70 mm, the spherical surface refractive power is −2.00D, the refractivepower in the direction of astigmatism is −4.00D, the astigmatic dioptricpower is −2.00D, the first surface (which is the outer surface) is aspherical surface, and the second surface (which is the inner surface)is a toric surface. TABLE 1 Conventional example of lens data Externaldiameter (mm) 70.0 Center thickness (mm) 1.1 Refractive index 1.665First surface curvature (diopter) 1.661 Second surface curvature(diopter) y direction −3.663 Second surface curvature (diopter) zdirection −5.663 Second surface aspherical surface coefficients A₄₀0.000E + 00 (A mn) A60 0.000E + 00 A₈₀ 0.000E + 00 A₂₂ 0.000E + 00 A₄₂0.000E + 00 A₆₂ 0.000E + 00 A₀₄ 0.000E + 00 A₂₄ 0.000E + 00 A₄₄ 0.000E +00 A₀₆ 0.000E + 00 A₂₆ 0.000E + 00 A₀₈ 0.000E + 00

FIG. 3 is a distribution diagram of the mean residual refractive powererror ΔPav in the conventional example of an astigmatic lens shown inTable 1. The central portions of the small circles in the figureindicate the positions where the principal rays pass through therespective points within the lens plane, and the sizes of the smallcircles express the magnitude of the mean residual refractive powererror ΔPav in the respective principal rays. As is seen from FIG. 3, thevalue of the mean residual refractive power error ΔPav increases fromthe center of the lens toward the peripheral portions of the lens.

FIG. 4 is a distribution diagram of the residual mean refractive powererror AMP in the conventional example of an astigmatic lens shown inTable 1. The central portions of the small circles in the figureindicate the positions where the principal rays pass through therespective points within the lens plane, and the sizes of the smallcircles express the magnitude of the residual mean refractive powererror ΔMP in the respective principal rays. Furthermore, in cases wherethe small circles are drawn by means of solid lines, this indicates thatΔMP has a positive value, and in cases where the small circles are drawnby means of dotted lines, this indicates that ΔMP has a negative value.As is seen from FIG. 4, the value of the residual mean refractive powererror ΔMP increases from the center of the lens toward the peripheralparts of the lens.

FIG. 5 is a distribution diagram of the residual astigmatic aberrationΔAS in the conventional example of an astigmatic lens shown in Table 1.The central portions of the small circles in the figure indicate thepositions where the principal rays pass through the respective pointswithin the lens plane, and the sizes of the small circles express themagnitude of the residual astigmatic aberration ΔAS in the respectiveprincipal rays. Furthermore, the straight lines within the small circlesindicate the meridian direction of the maximum residual refractive powererror ΔPmax for the minimum principal direction of the eye. As is seenfrom FIG. 5, the value of the residual astigmatic aberration ΔASincreases conspicuously from the center of the lens toward theperipheral parts of the lens.

Table 2 shows lens data for an embodiment of the present invention inwhich the external diameter of the lens is 70 mm, the spherical surfacerefractive power is −2.00D, the refractive power in the astigmaticdirection is −4.00D, the astigmatic dioptric power is −2.00D, the firstsurface (which is the outer surface) is a spherical surface, and thesecond surface (which is the inner surface) is an aspherical toricsurface.

This embodiment of the present invention is a result of automatedoptimization calculations in which the mean residual refractive powererror ΔPav was viewed as being especially important, the system wasdevised so that this value was minimized, and the calculations werefurther performed using the residual astigmatic aberration ΔAS and theresidual mean refractive power error ΔMP as parameters for optimizationso that these values were also as small as possible.

Specifically, the mean residual refractive power error ΔPav wasminimized, and in this case, if the residual astigmatic aberration ΔASand residual mean refractive power error AMP were within permissibleranges, it was considered that a solution was obtained. On the otherhand, if the residual astigmatic aberration ΔAS and the residual meanrefractive power error ΔMP were not within permissible ranges, stepswere taken so that the mean residual refractive power error ΔPav wasincreased to a value slightly greater than the minimum value, thusensuring that the residual astigmatic aberration ΔAS and residual meanrefractive power error AMP were ultimately within permissible ranges.Furthermore, in the calculations, it was assumed that a=0 and b=π.

Furthermore, the descriptive equation of the aspherical portion used inthe second surface in the present embodiment was as shown below.$\begin{matrix}{ϰ = {\Sigma\quad A_{mn}y^{m}z^{n}}} \\{= {A_{00} + {A_{01}z^{1}} + {A_{02}z^{2}} + \ldots + {A_{10}y^{1}} + {A_{11}y^{1}z} + {A_{12}y^{1}z^{2}} + \ldots}}\end{matrix} + {A_{20}y^{2}A_{21}y^{2}z^{1}} + {A_{22}y^{2}z^{2}} + \ldots + {A_{mn}y^{m}z^{n}}$

Accordingly, the second surface in this embodiment of the presentinvention has a shape obtained by adding an aspherical surface shapeusing the values of the aspherical surface coefficients described inTable 2 in the aspheric surface descriptive equation described above tothe toric surface constituting the basis. TABLE 2 Example of lens datafor embodiment External diameter (mm) 70.0 Center thickness (mm) 1.1Refractive index 1.665 First surface curvature (diopter) 1.661 Secondsurface curvature (diopter) y direction −3.663 Second surface curvature(diopter) z direction −5.663 Second surface aspherical surfacecoefficients A₄₀ −2.488E-07 (A mn) A₆₀ 7.511E-11 A₈₀ −1.192E-14 A₂₂−5.123E-07 A₄₂ 7.317E-11 A₆₂ −1.732E-17 A₀₄ −4.801E-07 A₂₄ 2.186E-10 A₄₄1.991E-14 A₀₆ 1.810E-10 A₂₆ −3.803E-14 A₀₈ −3.602E-14

FIG. 6 is a distribution diagram of the mean residual refractive powererror ΔPav of the astigmatic lens of the embodiment of the presentinvention shown in Table 2. The method of description is the same as inFIG. 3. As is seen from this figure, the value of the mean residualrefractive power error ΔPav is suppressed to a small value over theentire surface of the lens.

FIG. 7 is a distribution diagram of the residual mean refractive powererror AMP in the astigmatic lens of the embodiment of the presentinvention shown in Table 2. The method of description is the same as inFIG. 4. As is seen from this figure, the value of the residual meanrefractive power error ΔMP is suppressed to a small value over theentire surface of the lens.

FIG. 8 is a distribution diagram of the residual astigmatic aberrationΔAS in the astigmatic lens of the embodiment of the present inventionshown in Table 2. The method of description is the same as in FIG. 5. Asis seen from this figure, the value of the residual astigmaticaberration ΔAS is suppressed to a small value over the entire surface ofthe lens.

Furthermore, the astigmatic dioptric power axes may inherently adoptvarious values according to the prescription of the user; in the abovedescription, however, in order to simplify the description, theprincipal meridian direction of the spherical surface dioptric power istaken in the vertical direction of the lens, and the principal meridiandirection of the astigmatic dioptric power is taken in the horizontaldirection of the lens. Nevertheless, it is clear that the presentinvention is effective regardless of the orientation of these astigmaticdioptric power axes.

In the embodiments described above, a spherical surface is used as thefirst surface, and a shape obtained by using the aspherical surfaceequation described above is used as the second surface. However, thepresent invention is not limited to such embodiments; it is clear thatthe present invention is effective for various shapes of the firstsurface and/or second surface, e.g., rotationally symmetrical asphericalsurface shapes in general and spline surface shapes.

Moreover, with regard to the working apparatus used in the presentinvention, any arbitrary apparatus that is ordinarily used in theworking of ophthalmic lenses may be appropriately used. Generally, in ashape working apparatus, the working of the refractive surfaces isperformed while causing relative movement of the ophthalmic lens andworking tool. Specifically, the shape working apparatus works the shapewhile controlling the amount of relative movement of the ophthalmic lensand working tool on the basis of the design data obtained by means ofthe present invention. Furthermore, an apparatus using a system whichhas a plurality of working tools, and which performs working whilechanging the working tool in accordance with the refractive surface thatis being formed, may also be used as the shape working apparatus.

1. A method for designing ophthalmic lenses in which at least onesurface among the set of refractive surfaces on the object side and eyeside in the mounted state has a spherical or aspherical surface shapethat is formed beforehand, and at least one refractive surface has anaspherical surface shape, this ophthalmic lens design method beingcharacterized in that design is performed so that the shape of therefractive surface whose shape is not formed beforehand among the set ofrefractive surfaces is an aspherical surface shape which is such thatthe aberration of the ophthalmic lens is corrected according to the lawsof Donders-Listing in accordance with at least the refractive power thatis necessary for refractive correction of the user or the refractivepower that is necessary for astigmatic correction, or both.
 2. Theophthalmic lens design method according to claim 1, which ischaracterized in that an arbitrary meridian of the refractive powernecessary for refractive correction of the user is taken as a standardmeridian in arbitrary principal rays passing through the plane of theophthalmic lens, and the shape of the refractive surface whose shape isnot formed beforehand is determined so that ΔPall expressed by Equation(1) below shows a minimum value or a specified value or less, where E(α)is the refractive power in the meridian direction that is required forthe refractive correction of the eye of the user in the meridiandirection at an arbitrary angle of α from the standard meridian, andD(α) is the refractive power in the meridian direction of the lens.ΔPall=∫ _(α) ^(b) |ΔP(α)|dα  (1) Here, ΔP(α) is a function expressed asΔP(α)=D(α)−E(α), and a and b are values that satisfy the equationb−a=nπ, where n is a natural number.
 3. The ophthalmic lens designmethod according to claim 1, which is characterized in that an arbitrarymeridian of the refractive power necessary for refractive correction ofthe user is taken as a standard meridian in arbitrary principal rayspassing through the plane of the ophthalmic lens, and the shape of therefractive surface whose shape is not formed beforehand is determined sothat ΔPav expressed by Equation (2) below shows a minimum value or aspecified value or less, where E(α) is the refractive power in themeridian direction that is required for the refractive correction of theeye of the user in the meridian direction at an arbitrary angle of αfrom the standard meridian, and D(α) is the refractive power in themeridian direction of the lens. $\begin{matrix}{{\Delta\quad{Pav}} = {\frac{1}{{b - a}}{\int_{a}^{b}{{{\Delta\quad{P(\alpha)}}}{\mathbb{d}\alpha}}}}} & (2)\end{matrix}$ Here, ΔP(α) is a function expressed as ΔP(α)=D(α)−E(α),and a and b are values that satisfy the equation b−a=nπ, where n is anatural number.
 4. The ophthalmic lens design method according to claim1, which is characterized in that an arbitrary meridian of therefractive power necessary for refractive correction of the user istaken as a standard meridian in arbitrary principal rays passing throughthe plane of the ophthalmic lens, and the shape of the refractivesurface whose shape is not formed beforehand is determined so that atleast one of the values ΔAS or ΔMP satisfying the following conditionalequations shows a minimum value or a specified value or less, whereΔPmax is the maximum value and ΔPmin is the minimum value ofΔP′(α)=D(α)−E(α) in the range of a ≦α≦b or b≦α≦a, with E(α) being therefractive power in the meridian direction that is required for therefractive correction of the eye of the user in the meridian directionat an arbitrary angle of α from the standard meridian, and D(α) beingthe refractive power in the meridian direction of the lens.Here, ΔAS=|ΔPmax−ΔPmin |  (3)ΔMP=(ΔPmax+ΔPmin)/2  (4) and a and b are values that satisfy theequation b−a=nπ, where n is an arbitrary integer excluding zero.
 5. Anophthalmic lens manufacturing method which is characterized in that thismethod has a process which is such that in a lens in which at least onesurface among the set of refractive surfaces on the object side and eyeside in the mounted state is a refractive surface having a spherical oraspherical surface shape that is formed beforehand, the shape of therefractive surface whose shape is not formed beforehand is designed inaccordance with the ophthalmic lens design method according to any oneof claims 1 through 4, and the refractive surface whose shape is notformed beforehand is worked in accordance with this design data.
 6. Amethod for manufacturing an ophthalmic lens using as an element materiala semi-product ophthalmic lens in which at least one surface among theset of refractive surfaces on the object side and eye side in themounted state is a refractive surface having a spherical or asphericalsurface shape that is formed beforehand, and at least one refractivesurface has an aspherical surface shape, this ophthalmic lensmanufacturing method being characterized in that this method has thesteps of attaching the semi-product ophthalmic lens to a shape workingapparatus, and working the refractive surface of the semi-product lenswhose shape has not been formed beforehand by means of the shape workingapparatus on the basis of design data obtained by the method accordingto any of claims 1 through 4 to produce a finished product.
 7. Theophthalmic lens manufacturing method according to claim 6, which ischaracterized in that the design data is determined at a differentlocation from the location where the shape working apparatus is present,and is transmitted to the location where the shape working apparatus ispresent via a communication device.
 8. A computer program whichdetermines the aspherical surface shape of the refractive surface of anophthalmic lens, this computer program being characterized in that thecalculation of the refractive power E(α) in the meridian directionrequired for refractive correction of the eye of the user in thedirection of a meridian at an arbitrary angle of a from the standardmeridian when an arbitrary meridian of the refractive power require forrefractive correction of the user is taken as the standard meridian isperformed for each arbitrary set of principal rays passing through theophthalmic lens, the calculation of the refractive power D(α) in themeridian direction of the lens is performed for each arbitrary set ofprincipal rays passing through the ophthalmic lens, and the asphericalsurface shape of the refractive surface is determined on the basis ofE(α) and D(α) so that the aberration of the ophthalmic lens shows aminimum value or a specified value or less in accordance with the lawsof Donders-Listing.